Coils for generating uniform fields in a cylindrical ferromagnetic shield

A Helmholtz coil is widely used for generating uniform magnetic fields. On the other hand, a ferromagnetic shield is the most common method to eliminate external magnetic fields. However, if a Helmholtz coil is used inside a ferromagnetic shield, the uniform magnetic field generated by the coil is disturbed because of the influence of the ferromagnetic shield. This article presents a new coil system that generates highly uniform magnetic fields in any direction even inside a ferromagnetic shield. This coil system does not waste valuable space inside the shield, because the coils are placed so that they touch the inner surface of the shield. The magnetic fields generated by the system were numerically calculated and confirmed by experiments. For a cylindrical shield of radius R 0 with a ferromagnetic shielding disk at the bottom, the nonuniformity of the field is less than 1% within the space 0.7R 0 from the central axis and below 3R 0 from the top open edge of the shield.